common intersection of circles

[Tie Luo <tie@nus.edu.sg>]

Hi,
I am referring to your following email. Did you get answer? I know that email is quite old but I really also want to know the interesting result very much. Thanks!

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To: compgeom-discuss@research.bell-labs.com 
Subject: common intersection of circles 
From: Karthik Haridoss <karthik@utdallas.edu> 
Date: Thu, 19 Sep 2002 14:51:25 -0500 (CDT) 
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Hello computational poeople,

I have 3 circles, with their centers and radius known. How would I
compute the common area of intersection of the three circles. I am not
sure if my three circles are intersecting at all. If they are intersection
the area formula should give me the value of common area of intersection
else it should return 0. Please advise in that manner.I did a
brief search on NET and was able to find a sampling based method,
which takes a point in random and sees is the point is in the common
area and proceed accordingly. But I need a definitive formula based
approach. Can you please provide me the formula common area of
intersection of three circles. Also provide me links that has the software
implementation of this problem.

Please use this general equation of the circle
(X-a)^2 + (Y-b)^2 = r^2. Where (a,b) is the center of that cicle and r
is its radius.


Thanks in advance.

Happy day,
Karthik




_____________________________________________

Karthik Haridoss
Research Assistant
Dept. of Comp. Science
Univ. of Texas at Dallas
_____________________________________________

-- 
Regards,
 Tie
6/9/2005


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